共查询到20条相似文献,搜索用时 31 毫秒
1.
M. Ram Murty 《印度理论与应用数学杂志》2010,41(1):15-23
Let p be prime and q|p − 1. Suppose x
q
≡ a(mod p) has a solution. We estimate the size of the smallest solution x
0 with 0 < x
0 < p. We prove that |x
0| ≪ p
3/2
q
−1 log p. By applying the Burgess character sum estimates, and estimates of certain exponential sums due to Bourgain, Glibichuk and
Konyagin, we derive refinements of our result. 相似文献
2.
In this article, the authors establish the conditions for the extinction of solutions, in finite time, of the fast diffusive polytropic filtration equation u t ?=?div(|?u m | p?2?u m )?+?a∫Ω u q (y,?t)dy with a, q, m?>?0, p?>?1, m(p???1)?1, in a bounded domain Ω???R N (N?>?2). More precisely speaking, it is shown that if q?>?m(p???1), any non-negative solution with small initial data vanishes in finite time, and if 0?q?m(p???1), there exists a solution which is positive in Ω for all t?>?0. For the critical case q?=?m(p???1), whether the solutions vanish in finite time or not depends on the comparison between a and μ, where μ?=?∫?Ωφ p?1(x)dx and φ is the unique positive solution of the elliptic problem ?div(|?φ| p?2?φ)?=?1, x?∈?Ω; φ(x)?=?0, x?∈??Ω. 相似文献
3.
Let E = Eσ : y2 = x(x + σp)(x + σq) be elliptic curves, where σ = ±1, p and q are primenumbers with p+2 = q. (i) Selmer groups S(2)(E/Q), S(φ)(E/Q), and S(φ)(E/Q) are explicitly determined,e.g. S(2)(E+1/Q)= (Z/2Z)2, (Z/2Z)3, and (Z/2Z)4 when p ≡ 5, 1 (or 3), and 7(mod 8), respectively. (ii)When p ≡ 5 (3, 5 for σ = -1) (mod 8), it is proved that the Mordell-Weil group E(Q) ≌ Z/2Z Z/2Z,symbol, the torsion subgroup E(K)tors for any number field K, etc. are also obtained. 相似文献
4.
Massimo Giulietti 《Designs, Codes and Cryptography》2008,47(1-3):135-143
For any divisor k of q
4−1, the elements of a group of k
th-roots of unity can be viewed as a cyclic point set C
k
in PG(4,q). An interesting problem, connected to the theory of BCH codes, is to determine the spectrum A(q) of maximal divisors k of q
4−1 for which C
k
is a cap. Recently, Bierbrauer and Edel [Edel and Bierbrauer (2004) Finite Fields Appl 10:168–182] have proved that 3(q
2 + 1)∈A(q) provided that q is an even non-square. In this paper, the odd order case is investigated. It is proved that the only integer m for which m(q
2 + 1)∈A(q) is m = 2 for q ≡ 3 (mod 4), m = 1 for q ≡ 1 (mod 4). It is also shown that when q ≡ 3 (mod 4), the cap is complete.
相似文献
5.
We give a new proof of a theorem of P. Mihailescu which states that the equation x
p – y
q = 1 is unsolvable with x, y integral and p, q odd primes, unless the congruences p
q p (mod q
2) and q
p q (mod p
2) hold. 相似文献
6.
Huashui Zhan 《Applications of Mathematics》2008,53(6):521-533
We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation u
t
= div(u
m−1|Du|
p−2
Du) − u
q
with an initial condition u(x, 0) = u
0(x). Here the exponents m, p and q satisfy m + p ⩾ 3, p > 1 and q > m + p − 2.
The paper was supported by NSF of China (10571144), NSF for youth of Fujian province in China (2005J037) and NSF of Jimei
University in China. 相似文献
7.
San Ling 《Israel Journal of Mathematics》1993,84(3):365-384
Whenp, q are distinct odd primes, and γ:J
0(p)2×J
0(q)2→J
0(pq) is the natural map defined by the degeneracy maps, Ribet [10] determined the odd part of the kernel of γ. We study the 2-primary
part of this kernel through its intersection with the Eisenstein kernelJ
0(p)[I
p
)2×J
0(q)[I
q
]2. We determine this intersection forp≢1 mod 16,q≢1 mod 16, and also produce new elements of ker γ wheneverp≡9 mod 16 orq≡9 mod 16. These sharpen Ribet's results in [10]. 相似文献
8.
Let G = ℤ
p
, p an odd prime, act freely on a finite-dimensional CW-complex X with mod p cohomology isomorphic to that of a lens space L
2m−1(p; q
1, …, q
m
). In this paper, we determine the mod p cohomology ring of the orbit space X/G, when p
2 ∤ m. 相似文献
9.
Marco Buratti 《组合设计杂志》1995,3(1):15-24
In [2] R. C. Bose gives a sufficient condition for the existence of a (q, 5, 1) difference family in (GF(q), +)—where q ≡ 1 mod 20 is a prime power — with the property that every base block is a coset of the 5th roots of unity. Similarly he gives a sufficient condition for the existence of a (q, 4, 1) difference family in (GF(q, +)—where q ≡ 1 mod 12 is a prime power — with the property that every base block is the union of a coset of the 3rd roots of unity with zero. In this article we replace the mentioned sufficient conditions with necessary and sufficient ones. As a consequence, we obtain new infinite classes of simple difference families and hence new Steiner 2-designs with block sizes 4 and 5. In particular, we get a (p4α, 5, 1)-DF for any odd prime p ≡ 2, 3 (mod 5), and a (p2α, 4, 1)-DF for any odd prime p ≡ 2 (mod 3). © 1995 John Wiley & Sons, Inc. 相似文献
10.
P. S. Bruckman 《International Journal of Mathematical Education in Science & Technology》2013,44(4):554-555
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then xp ?≡?x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such that xm ?1?≡?1 (mod m), and if there exists no integer e?m???1 such that xe ?≡?1 (mod m), then m is prime. The new converse in question states the following: if p is any prime and xp ?≡?x (mod p), where x is known only to be algebraic, then x must be an integer (mod p). 相似文献
11.
Lisa A Mantini 《Journal of Functional Analysis》1985,60(2):211-242
Starting from the realization of the Fock space as L2-cohomology of p + q, 0,p(p + q) = ⊕m?m0,p(p + q), an integral transform is constructed which is a direct-image mapping from m0,p(p + q) into the space of holomorphic sections of some vector bundle Em over M ≈ U(p, q)/(U(q) × U(p)), m ? 0. The transform intertwines the natural actions of U(p, q) and is injective if m ? 0, so it provides a geometric realization of the ladder representations of U(p, q). The sections in the image of the transform satisfy certain linear differential equations, which are explicitly described. For example, Maxwell's equations are of this form if p = q = 2 and m = 2. Thus, this transform is analogous to the Penrose correspondence. 相似文献
12.
Edgar Karst 《BIT Numerical Mathematics》1967,7(2):114-122
In this paper 2
p
1 (modq),q=10p+1,p 3 (mod 4),p andq prime, is expressed uniquely (except for changes in sign and interchange ofx, y) in the formq=w
2+25 (x
2+y
2)/2+125z
2, 4wz=y
2–x
2–4xy, withw, x, y, z odd, forp<105. For 105<p<106, allp such that 2
p
1 (mod 10p + 1),p 3 (mod 4),p and 10p + 1 prime, are listed. 相似文献
13.
Let F be a finite simple undirected graph with no isolated vertices. Let p, q be prime numbers with p≥q. We complete the classification of the graphs on which a group of order pq acts edge-transitively. The results are the following. If Aut(Г) contains a subgroup G of order pq that acts edge-transitively on F, then F is one of the following graphs: (1) pK1,1; (2) pqK1,1; (3) pgq,1; (4) qKp,1 (p 〉 q); (5) pCq (q 〉 2); (6) qCp (p 〉 q); (7) Cp (p 〉 q = 2); (8) Cpq; (9) (Zp, C) whereC={±r^μ |μ∈Zq} withq〉2, q|(p-1) and r≠1≡r^q (modp); (10) Kp,1 (p 〉 q); (11) a double Cayley graph B(G,C) with C = {1-r^μ | μ ∈ Zq} and r≠1≡r^q (modp); (12) Kpq,1;or (13) Kp,q. 相似文献
14.
J. Feldman 《Israel Journal of Mathematics》1993,81(3):281-287
Letμ be a probability measure on [0, 1), invariant underS:x ↦px mod 1, and for which almost every ergodic component has positive entropy. Ifq is a real number greater than 1 for which logq/ logp is irrational, andT
n sendsx toq
nx mod 1, then for any ε>0 the measureμT
n
−1
will — for a set ofn of positive lower density — be within ε of Lebesgue measure. 相似文献
15.
Norman J. Finizio 《组合设计杂志》1995,3(2):135-146
Let E denote the group of units (i.e., the reduce set of residues) in the ring Z. Here we consider q,p to be primes, q ≡ 3 (mod 4), q ? 7, p ≡ 1 (mod 4). Let W denote a common primitive root of 3, q, and p2. If H denotes the (normal) subgroup of E that is generated by {?1, W}, we show that the factor group E/H is cyclic by demonstrating the existence of an element x in E such that the coset xH has order equal to |E/H|. This order is given by gcd(pn?1(p ? 1),q ? 1). This representation of E/H is exploited via an appropriate construction to produce Z-cyclic whist tournaments for 3qpn players. Consequently these results extend those of an early study of Wh(3qpn) that was restricted to gcd(pn?1(p ? 1),q ? 1) = 2. © 1995 John Wiley & Sons, Inc. 相似文献
16.
Tosis Kato 《Israel Journal of Mathematics》1972,13(1-2):135-148
Recently B. Simon proved a remarkable theorem to the effect that the Schrödinger operatorT=?Δ+q(x) is essentially selfadjoint onC 0 ∞ (R m if 0≦q ∈L 2(R m). Here we extend the theorem to a more general case,T=?Σ j =1/m (?/?x j ?ib j(x))2 +q 1(x) +q 2(x), whereb j, q1,q 2 are real-valued,b j ∈C(R m),q 1 ∈L loc 2 (R m),q 1(x)≧?q*(|x|) withq*(r) monotone nondecreasing inr ando(r 2) asr → ∞, andq 2 satisfies a mild Stummel-type condition. The point is that the assumption on the local behavior ofq 1 is the weakest possible. The proof, unlike Simon’s original one, is of local nature and depends on a distributional inequality and elliptic estimates. 相似文献
17.
Let X be a Banach space. We show that each m : ? \ {0} → L (X ) satisfying the Mikhlin condition supx ≠0(‖m (x )‖ + ‖xm ′(x )‖) < ∞ defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is isomorphic to a Hilbert space; each bounded measurable function m : ? → L (X ) having a uniformly bounded variation on dyadic intervals defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is a UMD space. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
19.
Wolfgang M. Ruppert 《Archiv der Mathematik》1999,72(1):47-55
Let f=a0(x)+a1(x)y+a2(x)y2 ? \Bbb Z[x,y]f=a_0(x)+a_1(x)y+a_2(x)y^2\in {\Bbb Z}[x,y] be an absolutely irreducible polynomial of degree m in x. We show that the reduction f mod p will also be absolutely irreducible if p 3 cm·H(f)emp\ge c_m\cdot H(f)^{e_m} where H (f) is the height of f and e1 = 4,e2 = 6, e3 = 6 [2/3]{2}\over{3} and em = 2 m for m S 4. We also show that the exponents em are best possible for m 1 3m\ne 3 if a plausible number theoretic conjecture is true. 相似文献
20.
Y. Wang In this paper, the finite time extinction of solutions to the fast diffusion system ut=div(|?u|p ? 2?u) + vm, vt=div(|?v|q ? 2?v) + un is investigated, where 1 < p,q < 2, m,n > 0 and is a bounded smooth domain. After establishing the local existence of weak solutions, the authors show that if mn > (p ? 1)(q ? 1), then any solution vanishes in finite time provided that the initial data are ‘comparable’; if mn = (p ? 1)(q ? 1) and Ω is suitably small, then the existence of extinction solutions for small initial data is proved by using the De Giorgi iteration process and comparison method. On the other hand, for 1 < p = q < 2 and mn < (p ? 1)2, the existence of at least one non‐extinction solution for any positive smooth initial data is proved. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献